Numerical solution of the Boltzmann equation with S-model collision integral using tensor decompositions

Direct Numerical Solution Of The Boltzmann Equation

Progress in computer hardware and improvement of numerical methods made solution of the Boltzmann equation for rather complex gas dynamic problems real. The method developed by the author is based on a projection technique for evaluation of the collision operator. The computed collision integral is conservative by density, impulse, and energy, and became equal to zero when the solution has a fo...

On the numerical solution of Urysohn integral equation using Legendre approximation

Urysohn integral equation is one of the most applicable topics in both pure and applied mathematics. The main objective of this paper is to solve the Urysohn type Fredholm integral equation. To do this, we approximate the solution of the problem by substituting a suitable truncated series of the well known Legendre polynomials instead of the known function. After discretization of the problem o...

Numerical Solution of the Boltzmann Equation I: Spectrally Accurate Approximation of the Collision Operator

Numerical solution of the wave equation using shearlet frames

In this paper, using shearlet frames, we present a numerical  method  for solving  the wave equation. We define a new shearlet system and by the Plancherel theorem, we calculate the shearlet coefficients.

Deterministic Numerical Solution of the Boltzmann Transport Equation

Due to its deterministic nature, the spherical harmonics expansion method is an attractive alternative to the Monte Carlo method for the solution of the Boltzmann Transport Equation for the purpose of electronic device simulation. However, since the problem is posed in a six-dimensional problem space emerging from the three-dimensional space variable and the three-dimensional momentum variable,...